Problem: Rewrite as a simplified fraction. ${1.91\overline{2} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1912.2222...\\ 100x &= 191.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1721}$ ${x = \dfrac{1721}{900}} \text{or} {1 \dfrac{821}{900}}$